Question

If A(1,2) B(4,3) and C(6,6) are the vertices of a parallelogram ABCD then find the co-ordinates of the fourth vertex

Answer 1

Let the 4th vertex be (x,y)
the mid point of AC is ((1+6)÷2,(2+6)÷2) =(7÷2,4)...i
Mid point of BD is ((4+x)÷2,(3+y)÷2)...ii
The diagonals of parallelogram bisect each other ,so the mid points of AC and BD would be same
so
from i ,ii 7÷2=(4+x)÷2 and 4=(3+y)÷2
=the coordinates of D are(3,5)

Answer 2

Answer:(3,5)

Step-by-step explanation:

Let coordinate be (x, y)

Taking mid point of AC. :

6+1/2= 7/2 and 6+2/2= 8/2= 4

Now, putting

4+x/2= 7/2

4+x = 7 (2 divided by 4+x/2 cut with 2 of 7/2)

x = 7-4

3

Now, 3+y/2 = 4

3+y = 4*2

3+y = 8

y = 8-3

y = 5